Question 1 Canadian viewers are interested to know if their home province is represented fairly in the Canada Games. The number of Canadians living in each province. according to the 2016 Census, can be found in the Excel sheet "Census". Provinces with smaller populations will be combined into regions. The six Canadian regions we will consider for the analysis are: 0 Alberta 0 Quebec 0 British Columbia 0 Atlantic Provinces 0 Prairie Provinces (New Brunswick, Nova Scotia, (Saskatchewan, Manitoba) Prince Edward island, a Ontario Newfoundiand and Labrador) Consider the men and women who competed in the 2013 and 2017 Individual Sprint Triathlon as a sample of all Canada Games athletes. a) Use the 2016 Census to construct a pie chart indicating the proportion of the population represented by each Canadian region. b) Use the 2013 and 2017 Individual Sprint Triathlon to construct a single pie chart indicating the proportion of all male and female triathletes represented by each Canadian region. (Hint: Also include the triathletes who did not finish the race.) Compare this pie chart to the pie chart in part a). What do you notice? c) Should we reject or not reject the claim that the distribution of triathletes' home provinces is representative of the Canadian population at the 5% significance level? (Hint: Use the result of a) and b) and apply the 2'2 test of goodness of fit.) Are there any regions that seem to be over or under represented? Question 2 Athletes are interested to know whether their Transition 1 time from swim to bike in a sprint triathlon is the same as in a super sprint triathlon. Consider the 2013 male triathletes who competed in both the Individual Sprint Triathlon (sprint) and in the Team Relay Triathlon (super sprint) as a sample of all male triathletes. Details of their race times can be found in the Excel sheet "2013 Men Sprint & Super Sprint". (Hint: The athlete's individual performance in a Team Relay is their Super Sprint data.) a) Consider the differences for Transition 1 times between a sprint triathlon and a super sprint triathlon. (Hint: The sample data are matched pairs. Explain why.) Find the sample mean and sample standard deviation for the differences. b) Is there enough evidence at the 10% significance level to conclude that the average Transition 1 time is different in a sprint than in a super sprint? (Hint: Use the results of a) and apply the t-test for difference of population means.) Provide a possible explanation for the difference you did or did not observe
